Related papers: Introduction to Focus Issue: Topics in Nonlinear S…
The study of nonlinear dynamics or chaos theory has emerged in the last three decades or so as an important interdisciplinary area of research encompassing a wide range of fields like: fluids, plasmas, biomedical sciences, finance,…
Nonlinear dynamics (``chaos theory'') and quantum mechanics are two of the scientific triumphs of the 20th century. The former lies at the heart of the modern interdisciplinary approach to science, whereas the latter has revolutionized…
Integrability and chaos are two of the main concepts associated with nonlinear physical systems which have revolutionized our understanding of them. Highly stable exponentially localized solitons are often associated with many of the…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian…
This Focus Issue Global Bifurcations, Chaos, and Hyperchaos Theory and Applications is dedicated to the 85th anniversary of the great mathematician, one of the founding fathers of dynamical chaos theory, Leonid Pavlovich Shilnikov.
The century of complexity has come. The face of science has changed. Surprisingly, when we start asking about the essence of these changes and then critically analyse the answers, the result are mostly discouraging. Most of the answers are…
The study of the phase space of multidimensional systems is one of the central open problems in dynamical systems. Being able to distinguish chaoticity from regularity in nonlinear dynamical systems, as well as to determine the subspace of…
We discuss some important issues arising from computational efforts in dynamical systems and fluid dynamics. Various individuals have misunderstood these issues since the onset of these problem areas; indeed, they have been routinely…
A reliable understanding of the Earth system is essential for the life quality of modern society. Natural hazards are the cause of most life and resource losses. The ability to define the conditions for a sustainable development of…
This work redefines the framework of chaos in dynamical systems by extending Devaney's definition to multiple mappings, emphasizing the pivotal role of nonlinearity. We propose a novel theorem demonstrating how nonlinear dynamics within a…
I briefly survey several fascinating topics in networks and nonlinearity. I highlight a few methods and ideas, including several of personal interest, that I anticipate to be especially important during the next several years. These topics…
Some of the so-called imponderables and counterintuitive puzzles associated with the Copenhagen interpretation of quantum mechanics appear to have alternate, parallel explanations in terms of nonlinear dynamics and chaos. These include the…
Nobel Prize laureate P.J.E. Peebles [24] has emphasized the importance and difficulties of studying the large scale clustering of matter in cosmology. Nonlinear gravitational instability plays a central role in understanding the clustering…
Electronics has changed greatly during recent decades, and some its basic concepts should be revisited. Starting from the sampling procedure, we consider some mathematical, physical and engineering aspects related to singular, mainly…
The standard nature of computing is currently being challenged by a range of problems that start to hinder technological progress. One of the strategies being proposed to address some of these problems is to develop novel brain-inspired…
The emerging field at the intersection of quantitative biology, network modeling, and control theory has enjoyed significant progress in recent years. This Special Issue brings together a selection of papers on complementary approaches to…
The study of synchronization of coupled systems is currently undergoing a major surge fueled by recent discoveries of new forms of collective dynamics and the development of techniques to characterize a myriad of new patterns of network…
Decentralization is a pervasive concept found across disciplines, including Economics, Political Science, and Computer Science, where it is used in distinct yet interrelated ways. Here, we develop and publicly release a general pipeline to…
Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…